(Ebook) Linear Algebra step by step 1st edition by Kuldeep Singh 0199654441 9780199654444

(Ebook) Linear Algebra step by step 1st edition by Kuldeep Singh 0199654441 9780199654444

Linear Algebra: step by step 1st edition by Kuldeep Singh - Ebook PDF Instant Download/DeliveryISBN:  0199654441, 9780199654444 

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ISBN-10 :  0199654441 

ISBN-13 : 9780199654444

Author:   Kuldeep Singh 

Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader's confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading players in the field of linear algebra to provide context for the topics covered. The dynamic and engaging style of the book includes frequent question and answer sections to test the reader's understanding of the methods introduced, rather than requiring rote learning. When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, in both professional and academic life. It will appeal to undergraduate students in mathematics, the physical sciences and engineering.

Linear Algebra: step by step 1st Table of contents:

1 Linear Equations and Matrices
1.1 Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Vector Arithmetic
1.4 Arithmetic of Matrices
1.5 Matrix Algebra
1.6 The Transpose and Inverse of a Matrix
1.7 Types of Solutions
1.8 The Inverse Matrix Method
Des Higham Interview
2 Euclidean Space
2.1 Properties of Vectors
2.2 Further Properties of Vectors
2.3 Linear Independence
2.4 Basis and Spanning Set
Chao Yang Interview
3 General Vector Spaces
3.1 Introduction to General Vector Spaces
3.2 Subspace of a Vector Space
3.3 Linear Independence and Basis
3.4 Dimension
3.5 Properties of a Matrix
3.6 Linear Systems Revisited
Janet Drew Interview
4 Inner Product Spaces
4.1 Introduction to Inner Product Spaces
4.2 Inequalities and Orthogonality
4.3 Orthonormal Bases
4.4 Orthogonal Matrices
Anshul Gupta Interview
5 Linear Transformations
5.1 Introduction to Linear Transformations
5.2 Kernel and Range of a Linear Transformation
5.3 Rank and Nullity
5.4 Inverse Linear Transformations
5.5 The Matrix of a Linear Transformation
5.6 Composition and Inverse Linear Transformations
Petros Drineas Interview
6 Determinants and the Inverse Matrix
6.1 Determinant of a Matrix
6.2 Determinant of Other Matrices
6.3 Properties of Determinants
6.4 LU Factorization
Françoise Tisseur Interview
7 Eigenvalues and Eigenvectors
7.1 Introduction to Eigenvalues and Eigenvectors
7.2 Properties of Eigenvalues and Eigenvectors
7.3 Diagonalization
7.4 Diagonalization of Symmetric Matrices
7.5 Singular Value Decomposition

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